Posted by FEBIN on Monday, January 16, 2012 at 7:19pm.
the sum of the n termsof an ap whose first term is 5 and common difference is 36 is equal to the sum of 2n terms of another AP whose first term is 36 ans common difference is 5. Find n?

arithmetic  Reiny, Monday, January 16, 2012 at 11:11pm
sum of n terms of 1st = (n/2)(10 + 36(n1))
= (n/2)(36n  26)
sum of 2n terms of 2nd = (2n/2)(72 + 5(2n1))
= n(10n + 67)
(n/2)(36n  26) = n(10n + 67)
divide by n, and multiply by 2
36n  26 = 20n + 134
16n = 160
n = 10
check:
sum(10 for 1st) = 5(10 + 36(9)) = 1670
sum(20 for 2nd) = 10(72 + 19(5)) = 1670
all is good!
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